Found a dead starling. We left a dish of water out after this, as well as a tray with some stale bread. (Didn't know if it had died of thirst or exhaustion.) Heard something fluttering in the heating duct, so I left the basement light on, too.

Found a live starling hanging out near water dish, similar to first. I managed to walk up to it (after a very brief chase) and catch it with my hands. When my girlfriend opened the basement door, it managed to free itself and fly out.

Based on the third incident, it seems the "tameness" stems from exhaustion. Our best guess is that the gas-powered water and heating exhaust into an otherwise disused chimney with an improperly screened cap. (I haven't confirmed the existence of a chimney, but the exhaust ducts do lead into a brick column in the basement.)

Now I just have to figure out 1) how to aid any further birds that get in, and 2) how to screen the (assumed) chimney without trapping anything else inside. Any thoughts?

Update 2011-02-09: Discovered a starling in the dining room. There was birdshit everywhere. This was apparently due in part to it having eaten a good deal of my aloe plant, which is a laxative. *No idea* how it got into living space -- all the doors were closed.